1. Field of the Invention
This invention relates to strain wave gearing, and more particularly to an improved tooth profile of a flexspline and a circular spline in harmonic drive devices.
2. Prior Art
The original harmonic drive strain wave gearing was introduced by Musser in U.S. Pat. No. 2,906,143. A harmonic drive strain wave gear comprises a rigid circular spline having "n" teeth, a flexspline having fewer than "n" teeth ("n" being a positive integer) and being disposed in the circular spline, and a rotatable wave generator disposed in the flexspline to deform the flexspline into a lobed configuration, such as an oval shape, so as to force the flexspline into engagement with the circular spline at two points of the major axis of the formed ovaloid. The wave generator may include an oval cam plate and a bearing snugly mounted on the outer periphery of the camplate. The outer bearing is matingly inserted into the flexspline so as to deform it to the peripheral contour of the camplate. An input shaft attached to the camplate provides rotation thereto, causing the ovaloid configuration of the flexspline to be correspondingly rotated. During such rotation, the circular spline is induced to rotate relative to the flexspline by an amount proportional to the difference in the number of teeth between the flexspline and the circular spline. When an output shaft is arranged on either the flexspline or the circular spline, that output shaft is rotated very slowly in comparison to its input shaft. Such harmonic drive strain wave gearing has been utilized in machinery requiring a high reduction ratio.
A recent attempt at improved tooth profile design is shown in U.S. Pat. No. 4,823,638 to Ishikawa, wherein the engagement between the flexspline and the circular spline is deemed to be an approximation to that of a rack mechanism. The tooth profile of the engaging splines is defined by a transformation of an original curve by the application of a reduced 1/2 scale to a corresponding similar figure, that is, a mapping curve derived by a similarity transformation from the movement locus of the crest of the flexspline relative to the circular spline.
The design of the '638 gear tooth is therefore based on a simplified traditional rack mechanism approximation.
In fact, the gear teeth are not located on a simple linear rack. The circular spline teeth are located on a circle and the flexspline teeth are located on an oval surface formed by the wave generator. These two curved surfaces cause an inclination angle change between a tooth on the flexspline relative to the circular spline as the tooth moves into the engagement from the minor axis to the major axis. Such inclination angle is ignored when it is assumed that the circular spline and the flexspline are straight racks.
More recently in the referenced U.S. patent application Ser. No. 08/113,285 an improvement in flexspline tooth profiles was obtained by taking into account precessing of the tooth angle at the front and back of the tooth lobe as the oval wave generator is rotated.